- Tytuł:
- Point derivations for Lipschitz functions andClarkes generalized derivative
- Autorzy:
-
Demyanov, Vladimir
Pallaschke, Diethard - Powiązania:
- https://bibliotekanauki.pl/articles/1339173.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
point derivations
generalized directional derivative
Lipschitz functions - Opis:
- Clarke's generalized derivative $f^0(x,v)$ is studied as a function on the Banach algebra Lip(X,d) of bounded Lipschitz functions f defined on an open subset X of a normed vector space E. For fixed $x\in X$ and fixed $v\in E$ the function $f^0(x,v)$ is continuous and sublinear in $f\in Lip(X,d)$. It is shown that all linear functionals in the support set of this continuous sublinear function satisfy Leibniz's product rule and are thus point derivations. A characterization of the support set in terms of point derivations is given.
- Źródło:
-
Applicationes Mathematicae; 1996-1997, 24, 4; 465-474
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł